The inverse eigenvalue problem for quantum channels

Given a list of n complex numbers, when can it be the spectrum of a quantum channel, i.e., a completely positive trace preserving map? We provide an explicit solution for the n=4 case and show that in general the characterization of the non-zero part of the spectrum can essentially be given in terms of its classical counterpart - the non-zero spectrum of a stochastic matrix. A detailed comparison between the classical and quantum case is given. We discuss applications of our findings in the analysis of time-series and correlation functions and provide a general characterization of the peripheral spectrum, i.e., the set of eigenvalues of modulus one. We show that while the peripheral eigen-system has the same structure for all Schwarz maps, the constraints imposed on the rest of the spectrum change immediately if one departs from complete positivity.Comment: 16 page

Glass in the submarine section of the HSDP2 drill core, Hilo, Hawaii

The Hawaii Scientific Drilling Project recovered ~3 km of basalt by coring into the flank of Mauna Kea volcano at Hilo, Hawaii. Rocks recovered from deeper than ~1 km were deposited below sea level and contain considerable fresh glass. We report electron microprobe analyses of 531 glasses from the submarine section of the core, providing a high-resolution record of petrogenesis over ca. 200 Kyr of shield building of a Hawaiian volcano. Nearly all the submarine glasses are tholeiitic. SiO2 contents span a significant range but are bimodally distributed, leading to the identification of low-SiO2 and high-SiO2 magma series that encompass most samples. The two groups are also generally distinguishable using other major and minor elements and certain isotopic and incompatible trace element ratios. On the basis of distributions of high- and low-SiO2 glasses, the submarine section of the core is divided into four zones. In zone 1 (1079–~1950 mbsl), most samples are degassed high-SiO2 hyaloclastites and massive lavas, but there are narrow intervals of low-SiO2 hyaloclastites. Zone 2 (~1950–2233 mbsl), a zone of degassed pillows and hyaloclastites, displays a continuous decrease in silica content from bottom to top. In zone 3 (2233–2481 mbsl), nearly all samples are undegassed low-SiO2 pillows. In zone 4 (2481–3098 mbsl), samples are mostly high-SiO2 undegassed pillows and degassed hyaloclastites. This zone also contains most of the intrusive units in the core, all of which are undegassed and most of which are low-SiO2. Phase equilibrium data suggest that parental magmas of the low-SiO2 suite could be produced by partial melting of fertile peridotite at 30–40 kbar. Although the high-SiO2 parents could have equilibrated with harzburgite at 15–20 kbar, they could have been produced neither simply by higher degrees of melting of the sources of the low-SiO2 parents nor by mixing of known dacitic melts of pyroxenite/eclogite with the low-SiO2 parents. Our hypothesis for the relationship between these magma types is that as the low-SiO2 magmas ascended from their sources, they interacted chemically and thermally with overlying peridotites, resulting in dissolution of orthopyroxene and clinopyroxene and precipitation of olivine, thereby generating high-SiO2 magmas. There are glasses with CaO, Al2O3, and SiO2 contents slightly elevated relative to most low-SiO2 samples; we suggest that these differences reflect involvement of pyroxene-rich lithologies in the petrogenesis of the CaO-Al2O3-enriched glasses. There is also a small group of low-SiO2 glasses distinguished by elevated K2O and CaO contents; the sources of these samples may have been enriched in slab-derived fluid/melts. Low-SiO2 glasses from the top of zone 3 (2233–2280 mbsl) are more alkaline, more fractionated, and incompatible-element-enriched relative to other glasses from zone 3. This excursion at the top of zone 3, which is abruptly overlain by more silica-rich tholeiitic magmas, is reminiscent of the end of Mauna Kea shield building higher in the core

Unlawfully Present Aliens, Driver’s Licenses, and Other State-Issued ID: Select Legal Issues

[Excerpt] This report provides an overview of key legal issues raised by state laws regarding the denial or issuance of driver’s licenses and other forms of ID to unlawfully present aliens. It also addresses the legal issues raised by local governments issuing ID cards to unlawfully present aliens, as well as by state and local approaches to recognizing foreign-issued ID documents

Authority of State and Local Police to Enforce Federal Immigration Law

[Excerpt] This report discusses the authority of state and local law enforcement to assist in the enforcement of federal immigration law through the investigation and arrest of persons believed to have violated such laws. It describes current provisions in federal law that permit state and local police to enforce immigration law directly, analyzes major cases concerning the ability of states and localities to assist in immigration enforcement, and briefly examines opinions on the issue by the Office of Legal Counsel (OLC) within the Department of Justice. This report does not discuss legal issues raised by states and localities enacting their own immigration-related laws, including measures intended to supplement federal law through the imposition of additional criminal or civil penalties

Stratigraphy of the Hawai'i Scientific Drilling Project core (HSDP2): Anatomy of a Hawaiian shield volcano

The Hawai'i Scientific Drilling Project (HSDP2) successfully drilled ∼3.1 km into the island of Hawai'i. Drilling started on Mauna Loa volcano, drilling 247 m of subaerial lavas before encountering 832 m of subaerial Mauna Kea lavas, followed by 2019 m of submarine Mauna Kea volcanic and sedimentary units. The 2.85 km stratigraphic record of Mauna Kea volcano spans back to ∼650 ka. Mauna Kea subaerial lavas have high average olivine contents (13 vol.%) and low average vesicle abundances (10 vol.%). Most subaerial Mauna Kea flows are ‘a‘ā (∼63%), whereas the Mauna Loa section contains nearly equal amounts of pāhoehoe and ‘a‘ā (like its current surface). The submarine Mauna Kea section contains an upper, ∼900 m thick, hyaloclastite-rich section and a lower, ∼1100 m thick, pillow-lava-dominated section. These results support a model that Hawaiian volcanoes are built on a pedestal of pillow lavas capped by rapidly quenched, fragmented lava debris. The HSDP2 section is compared here to a 1.7 km deep hole (SOH1) on Kilauea's lower east rift zone. Differences in the sections reflect the proximity to source vents and the lower magma supply to Kilauea's rift zone. Both drill core sections are cut by intrusions, but the higher abundance of intrusions in SOH1 reflects its location within a rift zone, causing more extensive alteration in the SOH1 core. The HSDP2 site recovered a relatively unaltered core well suited for geochemical analyses of the single deepest and most complete borehole ever drilled through a Hawaiian or any other oceanic island volcano

Stratospheric chemistry and transport

A Chemical Tracer Model (CTM) that can use wind field data generated by the General Circulation Model (GCM) is developed to implement chemistry in the three dimensional GCM of the middle atmosphere. Initially, chemical tracers with simple first order losses such as N2O are used. Successive models are to incorporate more complex ozone chemistry